Existence of magic rectangle sets over finite abelian groups

2024/10/31 by Yu, Shikang, Feng, Tao, Liu, Hengrui
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.23662

Abstract

Let a, b and c be positive integers. Let (G,+) be a finite abelian group of order abc. A G-magic rectangle set MRS_G(a,b;c) is a collection of c arrays of size a× b whose entries are elements of a group G, each appearing exactly once, such that the sum of each row in every array equals a constant γ∈ G and the sum of each column in every array equals a constant δ∈ G. This paper establishes the necessary and sufficient conditions for the existence of an MRS_G(a,b;c) for any finite abelian group G, thereby confirming a conjecture presented by Cichacz and Hinc.

Related

• On a conjecture by Sylwia Cichacz and Tomasz Hinc, and a related problem
• Magic partially filled arrays on abelian groups
• Magic squares on Abelian groups
• Introducing n-Magic Groups and Characterizing 3-Magic Finitely Generated Abelian Groups
• Magic rectangles with empty cells